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BetterGrades Algebra · Unit A6 · Unit Hub

Unit A6: Exponents, Roots, and Power Structure

Introduce repeated multiplication, its inverse questions, and the first nonlinear families. How do repeated multiplication and roots create new structures?

Act VI - Leaving constant additive change

The 9-lesson path

Exponent laws are derived from repeated factors; zero and negative exponents preserve those laws; roots reverse powers; simple power equations and graphs reveal behavior unlike lines.

Governing question

How do repeated multiplication and roots create new structures?

Introduce repeated multiplication, its inverse questions, and the first nonlinear families.

Mastery design

Know when to continue

Students justify exponent laws from repeated multiplication and solve mixed exact powerroot\frac{power}{root} equations.

Unit outcomes
  1. Interpret integer exponents and negative bases.
  2. Derive and apply exponent laws.
  3. Explain zero and negative exponents.
  4. Interpret roots and solve simple power equations.
  5. Compare linear, quadratic, cubic, and root patterns.
Core sequence

Lessons

Move in order when this material is new; use prerequisites and repair links when entering mid-unit.

  1. 01Exponents as repeated multiplicationDistinguish base, exponent, factors, and value.
  2. 02Negative bases and groupingDistinguish negation from raising a negative base to a power.
  3. 03Product and quotient lawsCombine powers with a common base by counting repeated factors.
  4. 04Power of a power, product, and quotientTrack how an outer exponent applies to every factor.
  5. 05Zero and negative exponentsDefine exponents beyond positive integers by preserving established laws.
  6. 06Scientific notationRepresent scale with a normalized coefficient and power of ten.
  7. 07Square roots and nth rootsTreat roots as inverse questions with principal-root conventions.
  8. 08Simple power and root equationsFind all real values whose power equals a target and check by substitution.
  9. 09Power-function previewCompare tables and graphs of x, x2,x3,x^2, x^3, and sqrt(x).

Practice around the path

Review, mixed practice, mastery, and investigation

Every route contains a fixed set of concrete questions, with detailed solutions available after an attempt.

ReviewCumulative reviewRevisit this unit with prior-unit retrieval.PracticeMixed practiceClassify the structure before choosing a method.MasteryMastery checkUse the supplied grading and cumulative-share contract.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

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